In his first meeting as president with his Mexican counterpart, Donald Trump on Friday said he "absolutely" intends for Mexico to pay for the controversial wall he wants to build along the United States' southern border, setting off a furor in Mexico over a goal his own administration has largely abandoned.

(latimes) -- Trump and Mexican President Enrique Peña Nieto met on the sidelines of the Group of 20 summit here, amid sharp disagreements over trade and immigration. Some officials had hoped the brief encounter could help heal badly strained relations between the two neighbors.

The proposed wall continues to make that difficult.

As journalists were allowed in to see the two leaders take their seats, one reporter asked Trump if he still wanted Mexico to pay for the wall.

"Absolutely," Trump said.

Mexico has repeatedly said it will not pay for a new border barrier, and Trump’s words set off a furious reaction in Mexico City.

Mexican officials, however, decided to ignore the remark, at least publicly.

Peña Nieto didn’t hear Trump’s exchange with the reporter, and there was no further discussion of the wall in the private talks that followed, Mexican officials said.

The wall “was not part of the conversation,” Mexican Foreign Minister Luis Videgaray said in a news conference here. “That’s what we had agreed to, and that’s how it was.”

Whether Peña Nieto and his delegation really didn’t hear the comment, Mexican officials were privately angry that Trump responded the way he did. The president easily could have ignored the question, one Mexican official said. A little more than an hour after the meeting with the Mexican delegation, Trump ignored reporters’ questions at the opening of his meeting with Russian President Vladimir Putin.

Trump’s statement was consistent with the campaign rhetoric, but not with what his administration actually has done. In March, the administration asked Congress for $4.1 billion to begin construction on additional border fencing and walls, conceding that Mexico would not be paying for it.

“It’s coming out of the Treasury,” Trump’s budget director, Mick Mulvaney, told reporters when asked who would pay for the wall. So far, that request has met with a chilly reception on Capitol Hill.

Homeland Security Department officials have made clear that the administration does not intend to build a wall along the full length of the border, the way Trump often has described it. There are already about 600 miles of wall, fencing or other blocking constructions along the 2,000-mile border, which traverses rivers, desert and hilly terrain.

Homeland Security Secretary John Kelly testified earlier this year that there would be no wall “from sea to shining sea,” and officials have said the focus will be on additional border fortifications in or near urban areas, most likely more fences than walls.

Videgaray said most of the 40-minute meeting was dedicated to the landmark 1994 North American Free Trade Agreement, which Trump initially panned as a terrible deal for the United States and threatened to pull out of, but now says he is willing to re-negotiate.

Talks begin Aug. 16, and Videgaray said the parties agreed to try to reach terms by the end of the year. (Mexico prefers to use the word “modernize” rather than “re-negotiate.”) Canada is also a signatory.

In his recorded weekly radio address, however, which was released Friday, Trump angrily denounced countries that have "gotten rich" by destroying American jobs, and called for a "total re-negotiation" of NAFTA, once again saying something in public that goes well beyond what his administration has actually proposed.

"If we don't get it, we will terminate, that is, end, NAFTA forever," Trump said.

Videgaray also said the two governments agreed to explore ways to “promote” farm jobs for temporary workers, a program that has existed for decades and allows thousands of Mexicans annually to travel to the United States legally to plant and harvest crops. Mexico has worried that the workers might get caught up in the Trump administration’s efforts to reduce immigration.

Before Trump responded to the reporter's question on Friday, the two presidents delivered prepared statements.

Trump referred to Peña Nieto as a "friend." In addition to NAFTA, he was negotiating “some other things with Mexico, and we’ll see how it all turns out, but I think we've made very good progress," he said.

Speaking through a translator, Peña Nieto said the meeting would help the two countries continue a "flowing dialog" especially "for the security of both nations, especially for our borders."

He noted that "migration" is an issue of concern to both administrations. And he added that "it is the co-responsibility to deal with organized-crime issues."

Videgaray confirmed that these issues came up in the private talks, although the emphasis was on NAFTA. The White House said after the meeting that the two presidents also discussed “regional challenges, including drug trafficking, illegal migration, and the crisis in Venezuela.”

Trump has been controversial in Mexico since the day he declared his candidacy and characterized many Mexicans as rapists and criminals who should be kept out of the U.S. Opposition to Mexican immigration to the U.S. became a hallmark of his campaign.

Though enduring a brutal wave of violence, some of it related to drug trafficking, Mexico is nevertheless one of the United States' largest trading partners, shares long and strong cultural ties and enjoyed relatively good diplomatic relations and security cooperation with Washington before Trump took office.

The two presidents met last August when Trump was a candidate. He traveled to Mexico City in a visit that many Mexicans saw as disastrous. Trump contradicted Peña Nieto on the wall and seized control of a news conference, calling on American reporters and ignoring the Mexicans as the Mexican president looked on helplessly.

In January, Peña Nieto canceled a scheduled first meeting when Trump threatened to impose a tax on Mexican imports to pay for the wall.

The two have also shared several telephone calls, some quite contentious. In one, according to an official account that became public, Trump suggested that he'd send U.S. troops to Mexico to fight drug traffickers if Mexico's army didn't step up. Nothing could be more anathema to Mexicans' sense of sovereignty and nationalism.

Even before Friday's encounter, expectations in Mexico were low that it would be a chance to reset the two governments' troubled relations. One prominent newspaper, El Financiero, said talking to Trump is a "conversation with a deaf man."

Despite the formal and public tension, other officials in the U.S. and Mexican governments are working more closely. Videgaray sustains a close relationship with presidential son-in-law and adviser Jared Kushner. Secretary of State Rex Tillerson and Kelly have traveled to Mexico City several times and received their counterparts in Washington.